Ronaldo has been in resurgent form after a slow start to the season and has scored 18 times in the league in 2018, plundering four goals in a 6-3 win over Girona in Real's last game.
He struck both goals in Portugal's 2-1 win over Egypt on March 21 and started the 3-0 defeat by the Netherlands on Monday.
Real trail runaway leaders Barcelona by 15 points and are third in the La Liga standings.
Spanish daily Marca said Ronaldo has agreed with coach Zinedine Zidane to remain in Madrid while his team mates make the two-and-a-half hour plane journey to the Canary Islands.
Ronaldo, 33, has started and scored in all eight of Real's Champions League games this season and is the runaway top scorer in the competition with 12 goals.
He has been persuaded to skip the occasional league game, particularly away from home, and was rested for Real's 2-1 win at Leganes and their 1-0 defeat at Espanyol in February
Ronaldo did not feature in any of his side's six games in the Kings Cup.
Real's quarter-final tie with Serie A leaders Juventus is a repeat of the 2017 Champions League final, which the Spanish side won 4-1 with two goals from Ronaldo.
(Reporting by Richard Martin, editing by Ed Osmond)
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